The present invention relates to a method and apparatus for measuring the optical parameters of phase objects. Specifically, the present invention provides a method and an apparatus that utilize the moirxc3xa9 effect, for determining the properties of various phase objects, particularly lenses.
Moirxc3xa9 patterns are generated whenever there is overlap between two periodic structures consisting of alternating transparent and opaque regions. For example, a simple moirxc3xa9 pattern is observed when two sets of equally spaced straight lines are superimposed on one another such that a small angle exists between the lines of the two sets.
The art suggests a variety of technical and scientific applications based on the moirxc3xa9 effect, including the use of said effect for determining the optical features of lenses.
Oster et al. [Scientific American 208, p. 54-63 (1963)] and Nishijima et al. [Journal of the Optical Society of America, 54(1), p. 1-5 (1964)] disclose the use of the moirxc3xa9 effect for testing lenses. According to the methods described in these publications, the lens is interposed between two gratings exhibiting the moirxc3xa9 pattern. The presence of the lens alters the moirxc3xa9 pattern observed, the degree and nature of the alternation being related to the focal length of the lens.
Benton et al. [Optical Engineering, 15(4), p. 328-331, (1976)], describe an interferometer for lens testing that is based on the moirxc3xa9 effect. The device comprises a point source and a pair of gratings, the lens to be tested being placed in front of the first grating.
Bolognini et al. [Optica Acta., 32(4), p. 409-422(1985)] describe interferometry based on the Lau effect. According to the optical arrangements discussed in the paper, the lens under test is positioned in the space between the gratings.
U.S. Pat. No. 4,459,027 discloses a method and an apparatus for mapping an optical object, using the moirxc3xa9 effect. The critical characteristic of the arrangement according to U.S. Pat. No. 4,459,027 is that collimated rays pass through the lens to be tested. This is accomplished by using coherent light, which in practice is provided by a laser point source, and by introducing means for collimating said light to produce collimated rays therefrom. The object to be tested, that is, the lens, is placed in the path of said collimated rays prior to reaching two gratings capable of generating a moirxc3xa9 pattern. The moirxc3xa9 pattern observed is analyzed in order to derive the optical parameters of the lens therefrom.
It is an object of the present invention to provide an efficient optical arrangement for measuring the properties of phase objects, particularly lenses, using simple and low-cost equipment.
It is another object of the present invention to provide an optical arrangement for measuring the properties of phase objects, utilizing simple mathematical procedures.
It is yet another object of the present invention to provide an optical set-up allowing accurate and sensitive mapping of position-dependent properties of phase objects.
The inventors have found that a unique optical arrangement may be effectively used to determine the optical properties of a phase object. This optical arrangement is characterized in that gratings used to generate moirxc3xa9 patterns are placed between a source of diffuse light and the object to be tested. The inventors have also surprisingly found that using this novel arrangement, the optical properties of interest, such as the power of a given lens, are linearly related to certain quantities derivable from the moirxc3xa9 pattern, and that the proportionality coefficient of said linear relation is a constant depending on the geometrical features of said arrangement.
Thus, in one aspect, the present invention provides a method for measuring the optical parameters of a phase object, comprising recording a moirxc3xa9 pattern viewed through said phase object, said moirxc3xa9 pattern being formed by illuminating by means of a source of diffuse light, first and second gratings positioned in the space between said light source and said phase object, wherein the plane of said first grating is parallel to the plane of said second grating, and calculating the optical parameters of interest from said moirxc3xa9 pattern.
The term xe2x80x9cphase objectxe2x80x9d as used herein refers to an object that neither absorbs light nor reflects it, but rather changes the phase of light or deflects it. Examples of phase objects that may be tested according to the present invention are lenses, glass plates, windshields, Perspex sheets, beamsplitters and goggles. The term xe2x80x9cphase objectxe2x80x9d, as used herein, also embraces any medium that exhibits changes in its refractive index. Such medium may be a liquid or a crystalline solid. In a particularly preferred embodiment of the invention the phase object to be tested is a lens. The lens to be tested may be of any type, including (but not limited to): spherical lens, cylindrical lens, toric lens, progressive lens and multifocal lens.
The term xe2x80x9cgratingxe2x80x9d, as used herein, refers to a periodic structure consisting of alternating transparent and opaque regions. Such grating may be provided in the form of a set of equally spaced straight lines, or in the form of a grid. Preferably, the first and second gratings are angularly oriented with respect to each other. According to a preferred embodiment of the invention, the first and second gratings are provided in the form of first and second grids, respectively, wherein each grid is obtained by overlapping two identical sets of equidistant parallel lines at an angle of 90xc2x0. Preferably, the periodicity of the sets of equidistant parallel lines forming the first grid is different from the periodicity of the sets of equidistant parallel lines forming the second grid.
The term xe2x80x9cperiodicityxe2x80x9d, when used herein in relation to the gratings, refers to the length of a single period within the grating. A grating""s period consists of an opaque region and the adjacent transparent region (e.g., the combined width of an opaque and adjacent transparent line). The term xe2x80x9cperiodicityxe2x80x9d, when used herein in relation to the fringes displayed by the moirxc3xa9 pattern, refers to the length of a single fringe""s period. One fringe period consists of a dark band and adjacent bright band observed in the moirxc3xa9 pattern. The term xe2x80x9cspatial frequencyxe2x80x9d, as used herein, is proportional to the inverse of periodicity, and is given by the number of grating periods, or fringe periods, per unit of length. Preferably, the unit of length is the entire width or height of the recorded moirxc3xa9 pattern. The spatial frequency may be conveniently expressed by means vector quantities in the spatial frequency plane, the scalar components of said vector quantities corresponding to the number of grating""s periods (or fringe periods) along the X and Y axes of said plane. These vector quantities are related to the second derivatives                     ∂        2            ⁢      D              ∂              x        2              ,                    ∂        2            ⁢      D              ∂              y        2              ,                    ∂        2            ⁢      D                      ∂        x            ⁢              ∂        y              ,                    ∂        2            ⁢      D                      ∂        y            ⁢              ∂        x            
of the wavefront of the beam exiting the phase object, which wavefront is designated D. The optical properties that are calculated according to the present invention depend linearly on the values of said derivatives.
According to a preferred embodiment of the invention, the gratings are illuminated by light that has been filtered, such that the light transmitted through the filter has a wavelength distribution in the form of a narrow band centered on a preselected wavelength xcex, and the two gratings are separated from each other by a distance d, given by d=nxc2x7p1p2/xcex, wherein n is an integer number (n=1, 2, 3 . . . ) and p1 and p2 indicate the periodicity of the first and second gratings, respectively.
According to a preferred embodiment of the invention, the recording of the moirxc3xa9 pattern generated between the images of the first and second gratings, said images being formed by the phase object, is effected by means of a camera focused at a plane between the gratings. Preferably, the camera is located at a predetermined distance from said gratings, such that, in the absence of the object to be tested, a desired reference moirxc3xa9 pattern consisting of horizontal and vertical fringes is captured by said camera, this reference pattern being distorted on introduction of the object to be tested.
According to a preferred embodiment of the invention, the calculation of the optical parameter of interest comprises transforming the recorded moirxc3xa9 pattern into one or more spots in the spatial frequency plane, said transformation being preferably effected by means of Fourier transform techniques, such that the vectors defining said spots are the vectors of spatial frequencies Vy and Vx associated with said moirxc3xa9 pattern, identifying the components of said vectors (Vyx, Vyy) and (Vxx, Vxy) and substituting their values in an equation which linearly relates said optical parameter of interest to the second order derivatives                     ∂        2            ⁢      D              ∂              x        2              ,                    ∂        2            ⁢      D                      ∂        x            ⁢              ∂        y              ,                    ∂        2            ⁢      D                      ∂        y            ⁢              ∂        x              ,                    ∂        2            ⁢      D              ∂              y        2              ,
respectively, wherein D is the wavefront of the beam exiting the phase object.
According to a preferred embodiment of the invention, the calculation of the optical parameter of interest is effected using an equation that linearly relates said optical parameter of interest to the second order derivatives                     ∂        2            ⁢      D              ∂              x        2              ,                    ∂        2            ⁢      D                      ∂        x            ⁢              ∂        y              ,                    ∂        2            ⁢      D                      ∂        y            ⁢              ∂        x              ,                    ∂        2            ⁢      D              ∂              y        2              ,
wherein D is the wavefront of the beam exiting the phase object, wherein the coefficient of proportionality k in said linear equation is given by k=p1/d, wherein d is the distance between the two gratings and p1 is related to the periodicity of said gratings and to the distances between said gratings and the camera used to record the moirxc3xa9 pattern.
According to a preferred embodiment of the invention, the coefficient of proportionality k is computed by plotting, for two or more calibration lenses whose powers are known, said powers as a function of one or more of the second order derivatives                     ∂        2            ⁢      D              ∂              x        2              ,                    ∂        2            ⁢      D                      ∂        x            ⁢              ∂        y              ,                    ∂        2            ⁢      D                      ∂        y            ⁢              ∂        x              ,                    ∂        2            ⁢      D              ∂              y        2              ,
wherein D is the wavefront of the beam exiting the phase object, for each calibration lens, to obtain a linear function, the slope of which equals k.
In another aspect, the present invention provides an apparatus for determining the optical properties of a phase object by means of moirxc3xa9 analysis, comprising:
A source for producing diffuse light;
First and second gratings capable of producing a moirxc3xa9 pattern, wherein said gratings are placed in the space between said light source and the position intended for said phase object, and the plane of said first grating is parallel to the plane of said second grating; and
Means for recording the moirxc3xa9 pattern viewed through said phase object.
Preferably, the apparatus comprises a suitable transparent support for placing the tested object thereon. Alternatively, the phase object is placed on the surface of the second grating, said surface being the surface facing the recording means. Preferably, the means for recording the moirxc3xa9 pattern comprises a camera positioned at a predetermined distance from the gratings. Preferably, the apparatus according to the present invention comprises calculation means for calculating from the moirxc3xa9 pattern photographed by the camera the optical properties of the phase object to be tested. Preferably, the apparatus comprises display means for representing the values of a position-dependent optical parameter of a phase object under test by means of a contour map corresponding to the surface of said object. The calculation means and display means may be provided in the form of an external computer, which is connected to the apparatus of the invention. Alternatively, said computer may be incorporated within the apparatus itself. Preferably, the apparatus according to the invention comprises filter means coupled to the source of diffuse light, to allow the transmission of a preselected wavelength. Preferably, the apparatus according to the invention comprises means positioned between the light source and the first grating, for uniformly projecting the diffuse light into the space between said light source and the phase object.